"Culture"?
If you are up and about on a Sunday morning, what about the church as San Jose with it's "Golden Altar" and see some of the real residents of Ibiza.
Alternatively, for island culture, get to San Carlos on a Saturday and visit the Las Dalias market and see some of the original hippy wares - each to their own, but I think it is much better than the Es Canar market on a Wednesday.
[/img]